## How Do You Measure a Triangle?

### Johnny WolfeSanta Rosa District Schools

#### Description

Student will discover angles and their relationship to triangles.

#### Objectives

Uses concrete and graphic models to derive formulas for finding rate, distance, time, angle measures and arc lengths.

Uses properties and relationships of geometric shapes to construct formal and informal proofs.

The student represents and applies geometric properties and relationships to solve real-world and mathematical problems.

#### Materials

- Overhead transparencies (if examples are to be worked on overhead) for How Do You Measure a Triangle? (see attached file).

- Graphing paper.

- Heavy duty paper.

- Paper fasteners.

- Protractor

- How Do You Measure a Triangle? Examples (see attached file).

- How Do You Measure a Triangle? Worksheet (see attached file).

- How Do You Measure a Triangle? Checklist (see attached file).

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for How Do You Measure a Triangle? Examples (see attached file).

2. Have marking pens (for overhead).

3. Have graphing paper.

4. Have heavy duty paper.

5. Have paper fasteners.

6. Have enough protractors for each student.

7. Have How Do You Measure a Triangle? Examples (see attached file) prepared and ready to demonstrate to students.

8. Have enough copies of How Do You Measure a Triangle? Worksheet (see attached file) for each student.

9. Have enough copies of How Do You Measure a Triangle? Checklist (see attached file) for each student.

#### Procedures

Prior Knowledge: Students should be familiar with the use of a protractor, the basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals and solving equations. Note: This lesson does not address the following: rate, distance time or arc lengths; formal proofs. This lesson contains a checklist to assist the teacher. The sole purpose of this checklist is to aide the teacher in identifying students that need remediation. Students who meet the “C” criteria are ready for the next level of learning. For grading purpose, the teacher may use the above scale or grade on a percentage correct.

1. Describe a triangle (see # 1 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

2. Discuss the parts of a triangle (see # 2 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

3. Discuss the relationship between an angle and its corresponding side (see # 3 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

4. Discus classifying triangles (see # 4 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

5. Describe an equiangular triangle (see # 5 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

6. Give students strips of heavy duty paper and paper fasteners. Have them investigate various types of triangles (see # 6 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

7. Discuss the parts of a right triangle (see # 7 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

8. Work example 8 (see attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

9. Discuss classifying triangles according to sides (see # 9 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

10. Discuss the parts of an isosceles triangle (see # 10 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

11. Work example 11 (see attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

12. Work example 12 (see attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

13. Work example 13 (see attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

14. Discuss Angle Sum Theorem (see # 14 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

15. Work example 15 (see attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

16. Work example 16 (see attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

17. Work a two column proof with students showing a Given and a Prove statement (see # 17 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

18. Give students an everyday example involving triangles. Also discuss interior and exterior angles (see # 18 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

19. Discuss the relationship between exterior and interior angles of a triangle (see # 19 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments (see attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

20. Discuss Exterior Angle Theorem (see # 20 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

21. Work example 21 (see attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

22. Discuss a corollary (see # 22 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

23. Prove the corollary “The acute angles of a right triangle are complementary” (see # 23 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

24. Prove the corollary “There can be at most one right or obtuse angle in a triangle” (see # 24 on attached file How Do You Measure a Triangle? Examples). Answer student questions and comments.

25. Distribute the How Do You Measure a Triangle? Worksheet (see attached file).

26. Distribute the How Do You Measure a Triangle? Checklist (see attached file). Describe what constitutes an “A,” “B,” “C,” “D,” and an “F” in the CHECKLIST.

27. The student will write their response on the worksheet.

28. The teacher will move from student to student observing the students work and lending assistance.

#### Assessments

Student worksheets will be taken up and scored according to “How Do You Measure a Triangle? Checklist”. These scores may be placed in the grade book.

#### Extensions

Ask students to draw any triangle with a straightedge and extend one side of the triangle to form an exterior angle. Have them label the exterior angle 1 and the two remote interior angles 2 and 3. Have them carefully cut out angle 2 and angle 3 and place them on angle 1. The cutout angles should show them that angle 1 is equal to the sum of angles 2 and 3.